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Article

Generalized Random Tunneling Algorithm for Continuous Design Variables

[+] Author and Article Information
Satoshi Kitayama

Department of Human Systems Engineering,  Kanazawa University, Kodatsuno 2-40-20, Kanawawa 920-8667, Japankitagon@t.kanazawa-u.ac.jp

Koetsu Yamazaki

Department of Human Systems Engineering,  Kanazawa University, Kodatsuno 2-40-20, Kanawawa 920-8667, Japan

J. Mech. Des 127(3), 408-414 (Jul 15, 2004) (7 pages) doi:10.1115/1.1864078 History: Received May 30, 2003; Revised July 15, 2004

This paper presents a global optimization method for continuous design variables. We call this method a generalized random tunneling algorithm (GRTA) because this method can treat the behavior constraints as well as the side constraints without using penalty parameters for the behavior constraints. The GRTA consists of three phases, that is, the minimization phase, the tunneling phase, and the constraint phase. In the minimization phase, local search technique, which is based on the gradient of the objective and constraint functions, is used. The objective of the tunneling phase is to find a point that improves the objective function obtained in the minimization phase. In the constraint phase, the feasibility of the point obtained in the tunneling phase is checked. By iterating these three phases, global or quasi-optimum may be obtained. Through mathematical and structural optimization problems, the validity and efficiency of the GRTA are examined.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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In case of satisfying constraints

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Search process by decreasing step size

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Change of search direction by random number

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Algorithm of the GRTA

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Contour of objective and constraint functions and search process

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Contour of objective and constraint functions and search process

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Optimum topology at global minimum

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(a) Optimum topology at local minimum, (b) optimum topology at local minimum

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The search process of example 4.1 by SA

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The search process of example 4.2 by SA

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The search process between the GRTA and SA

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The search region of the GRTA

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